Multivariate geostatistics: an introduction with applications ; with 7 tables
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| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Edition: | 3., completely rev. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | hier auch spätere unveränderte Nachdrucke |
| Physical Description: | XV, 387 Seiten Illustrationen, Diagramme |
| ISBN: | 3540441425 9783642079115 9783540441427 |
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| 100 | 1 | |a Wackernagel, Hans |d 1955- |e Verfasser |0 (DE-588)1228015775 |4 aut | |
| 245 | 1 | 0 | |a Multivariate geostatistics |b an introduction with applications ; with 7 tables |c Hans Wackernagel |
| 250 | |a 3., completely rev. ed. | ||
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XV, 387 Seiten |b Illustrationen, Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 650 | 4 | |a Geology -- Statistical methods | |
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Record in the Search Index
| _version_ | 1804129638520193024 |
|---|---|
| adam_text | Contents
1 Introduction
A From Statistics to Geostatistics 7
2 Mean, Variance, Covariance 9
The mean: center of mass........................... 9
Distribution function............................. 11
Expectation.................................. 12
Variance.................................... 13
Covariance .................................. 14
3 Linear Regression and Simple Kriging 15
Experimental covariance........................... 15
Linear regression............................... 16
Variance-covariance matrix.......................... 20
Multiple linear regression........................... 21
Simple kriging................................. 24
4 Kriging the Mean 27
Arithmetic mean and its estimation variance................. 27
Estimating the mean with spatial correlation................. 28
No systematic bias .............................. 29
Variance of the estimation error........................ 30
Minimal estimation variance......................... 30
Kriging equations............................... 31
Case of no correlation............................. 32
B Geostatistics 35
5 Regionalized Variable and Random Function 39
Multivariate time/space data ......................... 39
Regionalized variable............................. 40
Random variable and regionalized value................... 41
Random function............................... 41
Probability distributions............................ 42
Strict stationarity............................... 43
Stationarity of first two moments....................... 44
6 Variogram Cloud 45
Dissimilarity versus separation........................ 45
Experimental variogram............................ 47
Replacing the experimental by a theoretical variogram............ 48
7 Variogram and Covariance Function SO
Regional variogram.............................. 50
Theoretical variogram............................. 50
Covariance function.............................. 52
Positive definite function........................... 53
Conditionally negative definite function................... 53
Fitting the variogram with a covariance function............... 55
8 Examples of Covariance Functions 57
Nugget-effect model............................. 57
Exponential covariance function....................... 57
Spherical model................................ 58
Derivation of the spherical covariance.................... 58
9 Anisotropy 62
Geometric Anisotropy............................. 62
Rotating and dilating an ellipsoid....................... 62
Exploring 3D space for anisotropy...................... 64
Zonal anisotropy ............................... 65
Nonlinear deformations of space....................... 65
10 Extension and Dispersion Variance 66
Support.................................... 66
Extension variance .............................. 67
Dispersion variance.............................. 68
Krige s relation................................ 69
Change of support effect........................... 70
Change of support: affine model....................... 71
Application: acoustic data .......................... 73
Comparison of sampling designs....................... 76
11 Ordinary Kriging 79
Ordinary kriging problem........................... 79
Simple kriging of increments......................... 81
Block kriging................................. 82
XI
Simple kriging with an estimated mean.................... 84
Kriging the residual.............................. 85
Cross validation................................ 87
Kriging with known measurement error variance............... 88
12 Kriging Weights 89
Geometry................................... 89
Geometric anisotropy............................. 91
Relative position of samples ......................... 91
Screen effect.................................. 92
Factorizable covariance functions....................... 93
Negative kriging weights........................... 94
13 Mapping with Kriging 96
Kriging for spatial interpolation........................ 96
Neighborhood................................. 97
14 Linear Model of Regionalization 101
Spatial anomalies............................... 101
Nested variogram model ........................... 102
Decomposition of the random function.................... 103
Second-order stationary regionalization................... 104
Intrinsic regionalization............................ 105
Intrinsic regionalization with mostly stationary components......... 105
Locally stationary regionalization....................... 106
15 Kriging Spatial Components 107
Kriging of the intrinsic component...................... 107
Kriging of a second-order stationary component............... 108
Filtering.................................... 110
Application: kriging spatial components of arsenic data........... Ill
16 The Smoothness of Kriging 113
Kriging with irregularly spaced data..................... 113
Sensitivity to choice of variogram model................... 115
Application: kriging topographic data.................... 117
C Multivariate Analysis 121
17 Principal Component Analysis 123
UsesofPCA.................................. 123
Transformation into factors.......................... 123
Maximization of the variance of a factor................... 125
Interpretation of the factor variances..................... 126
Correlation of the variables with the factors................. 127
Xll
18 Canonical Analysis 137
Factors in two groups of variables ...................... 137
Intermezzo: singular value decomposition.................. 138
Maximization of the correlation........................ 138
19 Correspondence Analysis 140
Disjunctive table ............................... 140
Contingency table............................... 140
Canonical analysis of disjunctive tables ................... 141
Coding of a quantitative variable....................... 141
Contingencies between two quantitative variables.............. 141
Continuous correspondence analysis..................... 142
D Multivariate Geostatistics 143
20 Direct and Cross Covariances 145
Cross covariance function........................... 145
Delay effect.................................. 145
Cross variogram................................ 146
Pseudo cross variogram............................ 149
Difficult characterization of the cross covariance function.......... 150
21 Covariance Function Matrices 151
Covariance function matrix.......................... 151
Cramer s theorem............................... 151
Spectral densities............................... 152
Phase shift................................... 153
22 Intrinsic Multivariate Correlation 154
Intrinsic correlation model.......................... 154
Linear model ................................. 155
Codispersion coefficients........................... 156
23 Heterotopic Cokriging 158
Isotopy and heterotopy............................ 158
Ordinary cokriging.............................. 159
Simple cokriging............................... 161
24 Collocated Cokriging 165
Cokriging neighborhood ........................... 165
Collocated simple cokriging ......................... 166
Collocated ordinary cokriging ........................ 167
Simplification with a particular covariance model.............. 168
Xlll
25 Isotopic Cokriging 170
Cokriging with isotopic data......................... 170
Autokrigeability................................ 171
Bivariate ordinary cokriging ......................... 173
26 Multivariate Nested Variogram 175
Linear model of coregionalization...................... 175
Bivariate fit of the experimental variograms................. 177
Multivariate fit................................. 178
The need for an analysis of the coregionalization .............. 181
27 Case Study: Ebro Estuary 183
Kriging conductivity............................. 183
Cokriging of chlorophyll........................... 185
Conditional simulation of chlorophyll.................... 187
28 Coregionalization Analysis 194
Regionalized principal component analysis.................. 194
Generalizing the analysis........................... 195
Regionalized canonical and redundancy analysis............... 196
Cokriging regionalized factors........................ 196
Regionalized multivariate analysis...................... 197
29 Kriging a Complex Variable 200
Coding directional data as a complex variable................ 200
Complex covariance function......................... 200
Complex kriging ............................... 201
Cokriging of the real and imaginary parts .................. 202
Complex kriging and cokriging versus a separate kriging.......... 203
Complex covariance function modeling ................... 205
30 Bilinear Coregionalization Model 207
Complex linear model of coregionalization..................207
Bilinear model of coregionalization......................208
E Selective Geostatistics 211
31 Thresholds and Selectivity Curves 213
Threshold and proportion........................... 213
Tonnage, recovered quantity, investment and profit.............. 213
Selectivity................................... 216
Recovered quantity as a function of tonnage................. 217
Time series in environmental monitoring................... 219
XIV
32 Lognormal Estimation 221
Information effect and quality of estimators.................221
Logarithmic Gaussian model.........................223
Moments of the lognormal variable......................224
Lognormal simple kriging ..........................226
Proportional effect ..............................228
Permanence of lognormality .........................228
Stable variogram model............................233
Lognormal point and block ordinary kriging.................233
33 Gaussian Anamorphosis with Hermite Polynomials 238
Gaussian anamorphosis............................238
Hermite polynomials.............................239
Expanding a function into Hermite polynomials...............240
Probabilistic interpretation..........................240
Moments of a function of a Gaussian variable................241
Conditional expectation of a function of a Gaussian variable ........243
Empirical Gaussian anamorphosis......................244
Smoothing the empirical anamorphosis....................245
Bijectivity of Gaussian anamorphosis ....................247
34 Isofactorial Models 250
Isofactorial bivariate distribution....................... 250
Isofactorial decomposition.......................... 251
Isofactorial models.............................. 252
Choice of marginal and of isofactorial bivariate distribution......... 253
Hermitian and Laguerre isofactorial distributions.............. 254
Intermediate types between diffusion and mosaic models.......... 258
35 Isofactorial Change of Support 262
The point-block-panel problem........................ 262
Carrier s relation and point-block correlation................. 262
Discrete Gaussian point-block model..................... 266
General structure of isofactorial change-of-support............. 267
36 Kriging with Discrete Point-Bloc Models 273
Non-linear function of a block variable.................... 273
Conditional expectation and disjunctive kriging of a bloc.......... 274
Disjunctive kriging of a panel......................... 275
Uniform conditioning............................. 277
XV
F Non-Stationary Geostatistics 281
37 External Drift 283
Depth measured with drillholes and seismic................. 283
Estimating with a shape function....................... 284
Estimating external drift coefficients..................... 285
Cross validation with external drift...................... 290
Regularity of the external drift function ................... 294
Cokriging with multiple external drift .................... 296
Ebro estuary: numerical model output as external drift............ 297
Comparing results of conditional simulations and kriging.......... 297
38 Universal Kriging 300
Universal kriging system........................... 300
Estimation of the drift............................. 302
Underlying variogram and estimated residuals................ 303
From universal to intrinsic kriging...................... 306
39 Translation Invariant Drift 308
Exponential-polynomial basis functions................... 308
Intrinsic random functions of order k..................... 309
Generalized covariance function....................... 310
Intrinsic kriging................................ 311
Trigonometric temporal drift.......................... 312
Filtering trigonometric temporal drift..................... 312
Dual kriging.................................. 313
Splines..................................... 314
APPENDIX 317
Matrix Algebra 319
Linear Regression Theory 329
Covariance and Variogram Models 334
Additional Exercices 337
Solutions to Exercises 339
References 353
Bibliography 358
Index 381
|
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| physical | XV, 387 Seiten Illustrationen, Diagramme |
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| spelling | Wackernagel, Hans 1955- Verfasser (DE-588)1228015775 aut Multivariate geostatistics an introduction with applications ; with 7 tables Hans Wackernagel 3., completely rev. ed. Berlin [u.a.] Springer 2003 XV, 387 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier hier auch spätere unveränderte Nachdrucke Geologie Geology -- Statistical methods Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd rswk-swf Geostatistik (DE-588)4020279-3 gnd rswk-swf Geostatistik (DE-588)4020279-3 s Multivariate Analyse (DE-588)4040708-1 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010061599&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wackernagel, Hans 1955- Multivariate geostatistics an introduction with applications ; with 7 tables Geologie Geology -- Statistical methods Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Geostatistik (DE-588)4020279-3 gnd |
| subject_GND | (DE-588)4040708-1 (DE-588)4020279-3 |
| title | Multivariate geostatistics an introduction with applications ; with 7 tables |
| title_auth | Multivariate geostatistics an introduction with applications ; with 7 tables |
| title_exact_search | Multivariate geostatistics an introduction with applications ; with 7 tables |
| title_full | Multivariate geostatistics an introduction with applications ; with 7 tables Hans Wackernagel |
| title_fullStr | Multivariate geostatistics an introduction with applications ; with 7 tables Hans Wackernagel |
| title_full_unstemmed | Multivariate geostatistics an introduction with applications ; with 7 tables Hans Wackernagel |
| title_short | Multivariate geostatistics |
| title_sort | multivariate geostatistics an introduction with applications with 7 tables |
| title_sub | an introduction with applications ; with 7 tables |
| topic | Geologie Geology -- Statistical methods Multivariate analysis Multivariate Analyse (DE-588)4040708-1 gnd Geostatistik (DE-588)4020279-3 gnd |
| topic_facet | Geologie Geology -- Statistical methods Multivariate analysis Multivariate Analyse Geostatistik |
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